The effect of spherulitic truncation on small-angle light scattering

The effects of spherulitic truncation on the H_v small-angle light-scattering (SALS) patterns are determined by computer simulation of spherulite nucleation and growth. The simulation is carried out for simultaneous and sporadic nucleation of two-dimensional spherulites and simultaneous nucleation of three-dimensional spherulites. The scattered intensity differences between truncated spherulites and round spherulites are determined as functions of the type of growth and the volume (or area) fraction of spherulites. Methods for the determination of certain geometrical characteristics of spherulites systems by SALS are developed. These characteristics include the volume (or area). fraction of spherulites, the average spherulite radius, and the average spherulite volume (or area). The results of this study are essential in the quantitative analysis of H_v SALS from spherulitic systems. The simulation process is readily extendable to the examination of other morphological phenomena by SALS.     

Scattering structure factor of colloidal gels characterized by static light scattering, small-angle light scattering, and small-angle neutron scattering measurements

The scattering structure factor of a colloidal gel in a q range of 5 orders of magnitude has been determined by combining static light scattering, small-angle light scattering, and neutron scattering measurements. It exhibits simultaneously two types of structure information: a mass fractal scaling within the clusters that constitute the gel and a surface fractal scaling for length scales larger than that of the clusters. Such scattering behavior can be well interpreted by the pair-correlation function proposed in the literature to model an ideal structure constituted of mass fractal objects inside surface fractal objects.     

Monitoring coalescence behavior of soft colloidal particles in water by small-angle light scattering

The fractal dimension (D _f) of the clusters formed during the aggregation of colloidal systems reflects correctly the coalescence extent among the particles (Gauer et al., Macromolecules 42:9103, 2009). In this work, we propose to use the fast small-angle light scattering (SALS) technique to determine the D _f value during the aggregation. It is found that in the diffusion-limited aggregation regime, the D _f value can be correctly determined from both the power law regime of the average structure factor of the clusters and the scaling of the zero angle intensity versus the average radius of gyration. The obtained D _f value is equal to that estimated from the technique proposed in the above work, based on dynamic light scattering (DLS). In the reaction-limited aggregation (RLCA) regime, due to contamination of small clusters and primary particles, the power law regime of the average structure factor cannot be properly defined for the D _f estimation. However, the scaling of the zero angle intensity versus the average radius of gyration is still well defined, thus allowing one to estimate the D _f value, i.e., the coalescence extent. Therefore, when the DLS-based technique cannot be applied in the RLCA regime, one can apply the SALS technique to monitor the coalescence extent. Applicability and reliability of the technique have been assessed by applying it to an acrylate copolymer colloid.     

Mesoscopic structure formation in colloidal aggregation and gelation

Recent small-angle light scattering experiments have revealed that diffusively aggregating spherical particles develop structure on a mesoscopic length scale (∼ tens of particles). The mesoscopic structural length scale persists even when the aggregation proceeds to the formation of a space-spanning network (a gel). We review the technique of small-angle light scattering, survey the experimental evidence for mesoscopic structure formation, discuss attempts at understanding these experimental observations by computer simulation of irreversible and reversible diffusion-limited cluster aggregation (DLCA), and propose a coherent picture for the understanding of non-equilibrium aggregation in the context of phase transitions.     

In situ studies of monosaccharide gelation using the small-angle X-ray scattering time-resolved method

The process of gelation of one of the monosaccharides, alpha-galactose-based gelator, with benzene as a solvent, has been studied. Small-angle X-ray scattering (SAXS) synchrotron time-resolved measurements were performed throughout the gelation process. The obtained SAXS measurements were elaborated using such methods as the fractal analysis, Fourier transform to get distance distribution functions, and simulation of a cluster model. We obtained the picture of the mesostructure development from the sol state to the gel state. Our results indicate that the fractal-type aggregates exist in the sol and the process of gelation is accompanied by the structural transition. This transition causes the aggregates to become smaller and denser, and their shapes differ from those of the sol. The complex method of SAXS data treatment we established seems to be a useful tool also for further studies of monosaccharide gelation.     

In situ small-angle neutron scattering and rheological measurements of shear-induced gelation

The microscopic structure of shear-induced gels for a mixed solution of 2-hydroxyethyl cellulose and nanometer-size spherical droplets has been investigated by in situ small-angle neutron scattering (SANS) with a Couette geometry as a function of shear rate gamma. With increasing gamma, the viscosity increased rapidly at gamma approximately 4.0 s(-1), followed by a shear thinning. After cessation of shear, the system exhibited an extraordinarily large steady viscosity. This phenomenon was observed as a shear-induced sol-gel transition. Real-time SANS measurements showed an increase in the scattering intensity exclusively at low scattering angle region. However, neither orientation of polymer chains nor droplet deformation was detected and the SANS patterns remained isotropic irrespective of gamma. It took about a few days for the gel to recover its original sol state. A possible mechanism of gelation is proposed from the viewpoint of shear-induced percolation transition.     

Study of colloidal particle Brownian aggregation by low-coherence fiber optic dynamic light scattering

The aggregation kinetics of particles in dense polystyrene latex suspensions is studied by low-coherence fiber optic dynamic light scattering. Low-coherence fiber optic dynamic light scattering is used to measure the hydrodynamic radius of the aggregates. The aggregation kinetics data obtained can be fitted into a single exponential function, which is the characteristic of slow aggregation. It is found that the aggregation rate of particles increased with higher electrolyte levels and with larger particle concentrations. The experimental results can be explained by use of the Derjaruin-Landau-Verwey-Overbeer (DLVO) theory.     

The effect of crystallite shape on small-angle X-ray scattering

Summary Diffraction by a linear crystallite system was calculated to explain different shapes of small-angle reflections. The calculations show that various SAXS patterns observed can be obtained theoretically if the shape of certain crystallites are accounted for. Various reflection shapes can be explained chiefly by the changes in the crystallite shape and size. Dash, four-point and two-point reflections are associated with rectangular and oblique crystallite of small lateral dimensions. In the case of radial reflections the crystallite represents a plate and the fibril — a stack of plates. Structural changes in oriented samples with planar crystallite texture caused by shrinkage were studied. The principal process of shrinkage consists in the growth of lateral (with respect to the texture axis) crystallite dimensions and in their transformation into plates. Simultaneously the rotation of the macromolecule axis takes place. At the second stage of the shrinkage the layers twist around an axis perpendicular to the film plane. Then isotropic structure is formed. Transition between the two kinds of reflections are typical of various processes taking place in the course of polymer deformation and shrinkage.

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Zusammenfassung Die Röntgen-Beugung eines Systems aus linearen Kristalliten wurde berechnet, um verschiedene Formen von Kleinwinkelreflexionen zu erklären. Die Berechnungen zeigen, daß die beobachteten verschiedenen SAX-Beugungsbilder theoretisch erhalten werden können, wenn die Form der verschiedenen Kristallite in geeigneter Weise gewählt wird. Verschiedene Beugung kann im wesentlichen mit Änderungen von Kristallitgestalt und -große gedeutet werden. Strich-, 2-Punkt- und 4-Punkt-Beugung sind mit rechteckigen und plättchenförmigen Kristalliten von kleinen lateralen Dimensionen verknüpft. Im Fall von radialen Reflektionen ist der einzelne Kristallit ein Plättchen, und eine Fibrille ist ein Stapel von Plättchen. Strukturänderungen in orientierten Proben mit planarer Kristallittextur, erzeugt durch Schrumpfung, wurden studiert. Der Hauptvorgang bei Schrumpfung besteht im Wachsen der lateralen (mit Hinblick auf die Texturachse) Kristallit-dimensionen und in ihrer Überführung in Plättchen. Gleichzeitig findet eine Drehung der Achsen der Makromoleküle statt. Im 2. Stadium der Schrumpfung schrauben sich die Schichten um eine Achse senkrecht zur Filmebene. Dann bildet sich die isotrope Struktur. Der Übergang zwischen den beiden Arten von Beugungen ist für die verschiedenen Prozesse typisch, die im Laufe einer Deformation und einer Schrumpfung von Polymeren stattfinden.

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Dedicated to Prof.R. Hosemann on the occasion of his 60th birthday     

Multilayered adsorption of macrocations and macroanions on colloidal spheres as studied by dynamic light scattering measurements

The electrophoretic light scattering data on the thickness of the alternate multiple adsorption layers of macrocations and macroanions on the surfaces of colloidal spheres, which have been published by the authors in Colloid and Polymer Science (1999) 277;813, (2000) 278:380 and (2002) 280:533, are reexamined with help of the dynamic light scattering measurements. Colloidal silica spheres (110 nm in diameter) and monodispersed polystyrene spheres (220 nm) are used as colloidal spheres. The macrocations used are poly(4-vinyl- N- n-butylpyridinium bromide and poly(allylamine). Sodium poly(styrene sulfonate) and sodium polyacrylate are used as macroanions. It was clarified in the previous work that a very small amount of the large aggregates of the macroions coexists for most of the suspensions and the thickness values reported are large compared with the true values. The corrected thickness values support the continuous thin layer's growing adsorption of the macroions on the colloidal surfaces but do not support the expansion–contraction-type adsorption.     

Self-aggregation of mixtures of oppositely charged polyelectrolytes and surfactants studied by rheology, dynamic light scattering and small-angle neutron scattering

In this study, the phase behavior, structure and properties of systems composed of the cationic, cellulose-based polycation JR 400 and the anionic surfactants sodium dodecylbenzenesulfonate (SDBS) or sodium dodecylethoxysulfate (SDES), mainly in the semidilute regime, were examined. This system shows the interesting feature of a very large viscosity increase by nearly 4 orders of magnitude as compared to the pure polymer solution already at very low concentrations of 1 wt%. By using rheology, dynamic light scattering (DLS), and small-angle neutron scattering (SANS), we are able to deduce systematic correlations between the molecular composition of the systems (characterized by the charge ratio Z=[+(polymer)]/[?(surfactant)]), their structural organization and the resulting macroscopic flow behavior. Mixtures in the semidilute regime with an excess of polycation charge form highly viscous network structures containing rodlike aggregates composed of surfactant and polyelectrolyte that are interconnected by the long JR 400 chains. Viscosity and storage modulus follow scaling laws as a function of surfactant concentration (η~c(s)(4); G(0)~c(s)(1.5)) and the very pronounced viscosity increase mainly arises from the strongly enhanced structural relaxation time of the systems. In contrast, mixtures with excess surfactant charges form solutions with viscosities even below those of the pure polymer solution. The combination of SANS, DLS, and rheology shows that the structural, dynamical, and rheological properties of these oppositely charged polyelectrolyte/surfactant systems can be controlled in a systematic fashion by appropriately choosing the systems composition.     

Speckle reduction in the small-angle light scattering technique using sample vibration

Experimental patterns obtained using the small-angle light scattering technique for thin-film polymer studies are fraught with speckles arising from the effect of interspherulitic interference. The presence of speckles hampers efforts in characterizing the spherulitic structure. Using a divergent beam increases the number of scattering sites and results in a reduction of the degree of speckling. Nevertheless, this decimates the ability of analyzing the pattern at low-scattering angles. Employing an expanded collimated beam produces the same effect but necessitates the use of specially designed optical components. This article outlines a novel technique that involves simple vibration of the polymer sample. Experimental results confirm its efficacy in reducing speckles without limiting the ability for analysis at low-scattering angles. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 937–943, 1997     

Correlation between colloidal stability and surfactant adsorption/association phenomena studied by light scattering

The stability of a colloidal system composed of styrene-acrylate copolymer particles and potassium stearate (KS) anionic surfactant molecules has been determined in terms of the Fuchs stability ratio, W, as a function of the surfactant concentration, by measuring the initial aggregation kinetics using the small-angle light scattering (SALS) technique. The structure of the particle surface is peculiar, being irregularly patterned, and thus represents a model system to investigate colloidal stability of nonsmooth colloidal particles. From the SALS kinetic experiments, it is found that the stability increases dramatically with KS concentration until the saturation of the available surface occurs. At concentrations higher than the saturation concentration, the W value decreases markedly with KS, as a consequence of attractive depletion forces induced by formation of micelles in the water phase. The adsorption isotherm, determined through the surface tension technique, agrees with the W vs KS behavior, with respect to the onset of saturation and the surface-per-molecule value, and it can be described by the two-step Langmuir isotherm. Static light scattering spectra of the particles at different adsorbed amounts of KS have been fitted by means of the Lorenz-Mie theory and accounting for the experimentally determined particle size distribution. The increase in the particle diameter imputable to KS adsorption is sizable. Stability data measured under high fluid shear in a turbulent capillary (in the absence of any screening salt) fit well into this scenario. However, depletion forces are shown to be noncooperative with turbulent shear in the absence of screening electrolytes.     

Characterisation of structure and aggregation processes of aquatic humic substances using small-angle scattering and X-ray microscopy

Aquatic humic substances (HS), an important part of the dissolved organic carbon in freshwater systems, are polyfunctional natural compounds with polydisperse structure showing strong aggregation/coagulation behaviour at high HS concentrations and in the presence of metal ions. In this study, small-angle neutron scattering (SANS), small-angle X-ray scattering (SAXS) and X-ray microscopy (XRM) were applied to characterise the structure and aggregation processes of HS in solution. In SAXS and XRM the high brilliant synchrotron radiation was used as X-ray source. Applying small-angle scattering, information about the size distribution and shape of aquatic HS was obtained. Spherical HS units were found which were stable in a wide concentration range in a kind of "monomeric" state almost independent of pH and ionic strength. At higher concentrations they formed chain-like agglomerates or disordered HS structures. In studies on the coagulation behaviour of HS after addition of copper ions, a linear relationship between Cu(2+) concentration and the formation of large disordered HS-Cu(2+) agglomerates was obtained. By using X-ray microscopy, single "huge" particles were found in older solutions and in solutions with high HS concentrations. Over a threshold Cu(2+) concentration of approx. 300 mg/L, the formation of an extensive HS-Cu(2+) network structure was observed within a few minutes. The presented structures show the ability of the methods used to characterise processes between diluted phase and suspended matter, which play an important role particularly in the region of phase interfaces.     

Cholesteric hydroxypropylcellulose solutions: Microscopy and small-angle light scattering

Polarized optical microscopy and small-angle light scattering (SALS) are used to investigate the cholesteric phase of aqueous hydroxypropylcellulose (HPC) solutions. The results suggest a polygonal focal conic rather than the recently proposed parabolic focal conic morphology. Measurements of the polygonal domain size show it to decrease with increasing HPC concentration. Depolarized SALS gives clover-leaf patterns, whose maximum of intensity at 45° is related to the domain size.     

Assessment of small-angle and angle-averaged structure factor for monitoring electrostatic colloidal interactions using multiply scattered light

The isotropic scattering coefficients of 143-nm diameter polystyrene latex suspensions were measured using frequency-domain photon migration (FDPM) at 687 and 828 nm as a function of volume fraction (0.05-0.3) and ionic strength (1.0 to 120 mM NaCl equivalents) in order to derive the angle-integrated structure factor, S(q), and structure factor at zero wave vector, S(0). The effective surface charges of the dispersions were estimated by fitting the measured isotropic scattering coefficients at each wavelength as a function of volume fraction to the solution of the Orstein-Zernike integral equation using the hard sphere Yukawa potential model and mean spherical approximation as a closure relation. The estimates of surface charges were comparable at both wavelengths, but decreased with ionic strength. At 120 mM NaCl equivalents, the values of S(0) obtained from FDPM matched those predicted by the Percus-Yevick model, and decreased with volume fraction, consistent with prediction by the Carnahan-Starling equation.     

Dynamic light scattering and small-angle neutron scattering studies on organogels formed with a gelator

Small-angle neutron scattering (SANS) and light scattering studies were carried out on an organogel consisting of a gelator, coded P-1, and dimethyl sulfoxide (DMSO). The gelator was made of an oligosiloxane stem and about eight branches of an amino acid derivative combined with a long alkyl chain. The amino acid part, N-n-pentanoyl-L -isoleucylaminooctadecane, was responsible for intermolecular association via hydrogen bonding between amide groups. After the complete dissolution of P-1 in DMSO at 85 °C, the solution was cooled, and the variations of the scattered light intensity were monitored as a function of the temperature. The scattered intensity increased drastically at about 40 °C when the P-1 concentration (C) was 3.5 g/L, and this indicated gel formation. The SANS results showed that the scattering intensity function was a monotonically decreasing function, regardless of C. A master relationship of the scattering intensity was obtained with respect to C. These scattering studies disclosed the following facts. First, gelation could be monitored as an abrupt increase in the intensity. Second, the gel was composed of randomly oriented bundlelike clusters. Third, the structure factor could be reduced by the gelator concentration, and this indicated the presence of a self-similar structure across the gelation threshold. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1841–1848, 2004     

Quantitative determination of large structures by small-angle light scattering

A new small-angle light scattering camera has been developed. In contrast to conventional detection the present system is based on a recently developed two-dimensional charge-coupled-device chip made by Thomson (France). The advantage of this chip is its excellent linear response and very low dark signal even at room temperature. The best linearity was obtained by leading each pixel signal through the same amplifying system. The optical system covered a diffraction angular region from about 1° to 15° (q = 0.2–2.6 μm⁻¹). The camera was calibrated with grids and pinholes and was tested with polymer latex particles in solution and with spherulites from polymer films. Received: 06 December 1999 Accepted: 04 February 2000     

Determination of spherulite size distribution by small-angle light scattering

The theoretical backgrounds of the method of spherulite size distribution determination, on the basis of the small-angle light scattering technique, are presented. Special corrections of experimental data are introduced to achieve great accuracy of the determination of scattered light intensity distribution. Experiments have been done on low-density polyethylene samples obtained in various crystallization conditions. For these samples, the stepwise distributions of spherulite size have been determined.